Question

Find
the mean of the following
date
عملية
Frequency
less
less
less
Less
hess
than 20
than 40
than 6O
than 80
than 100
15
37
74
99
120​

Answer 1

$\huge{ \green{ \mathfrak{ \underline{Question}}}}$

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■☆Find the mean of the following data:☆■

$</p><p>\begin{tabular}{| c | l |}</p><p></p><p>\cline{1-2}</p><p></p><p>Class interval & Frequency \\</p><p></p><p>\cline{1-2}</p><p></p><p>Less than 20 & 15 \\</p><p></p><p>Less than 40 & 37 \\</p><p></p><p>Less than 60 & 74 \\</p><p></p><p>Less than 80 & 99 \\</p><p></p><p>Less than 100 & 120 \\</p><p></p><p>\cline{1-2}</p><p></p><p>\end{tabular}</p><p>$

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$\huge{ \green{ \mathfrak{ \underline{Answer}}}}$

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$\boxed{\red{\bold{Converting\: to\: class-intervals:}}}$

$</p><p>\begin{tabular}{| c | c | c | c |}</p><p></p><p>\cline{1-4}</p><p></p><p>Class-interval & Frequency(f_i) & class mark(x_i) & f_ix_i \\</p><p></p><p>\cline{1-4}</p><p></p><p>0 - 20 & 15 & 10 & 150 \\</p><p></p><p>20 - 40 & 22 & 30 & 660 \\</p><p></p><p>40 - 60 & 37 & 50 & 1850 \\</p><p></p><p>60 - 80 & 25 & 70 & 1750 \\</p><p></p><p>80 - 100 & 21 & 90 & 1890 \\</p><p></p><p>\cline{1-4}</p><p></p><p> & \Sigma f_i = 120 & & \Sigma f_ix_i = 6300 & </p><p></p><p>\cline{1-4}</p><p>\end{tabular}</p><p>$

$\boxed{\red{\bold{By\: direct \: method:}}}$

$\purple{\overline{X} = \displaystyle{\frac{ \Sigma f_ix_i}{\Sigma f_i}}}$

$\implies \overline{X} = \displaystyle{\frac{6300}{120}}$

$\green{\implies \overline{X} = 52.5}$

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